## 7. Integrals # Integrals Class 12 Maths

Get answers to all NCERT exercise questions, examples, supplementary exercise questions and Sample Papers with expert created video lecture, pdf notes and assignments for Integrals Class 12 Maths.

Summary:

Integration is the inverse process of differentiation. In the differential calculus, we are given a function and we have to find the derivative or differential of this function, but in the integral calculus, we are to find a function whose differential is given. Thus, integration is a process which is the inverse of differentiation.

Let $\frac{d}{dx}F(x) = f(x)$. Then, we write $\int{f(x) dx} = F(x) + C$. These integrals are called indefinite integrals or general integrals, C is called constant of integration. All these integrals differ by a constant.

From the geometric point of view, an indefinite integral is collection of family of curves, each of which is obtained by translating one of the curves parallel to itself upwards or downwards along the y-axis.

## Lectures for Integrals Class 12 Maths

• Lecture 1 and 2 are based on NCERT Exercises 7.1, 7.2 and 7.3
• These lectures also have questions from R. D. Sharma, NCERT Exemplar Problems, CBSE Question Bank (Support Material) and books from other states.

## Lecture - 1

This Lecture is based on First Method Direct Integration. This lecture has five parts with detailed explanation of concepts, derivations of all identities or formulas and explanation of sixty (60) practice questions from various books of integrals class 12 maths.

## Lecture - 2

This Lecture is based on Second Method Substitution. This lecture has eight parts with detailed explanation of concepts, derivations and eighty three (83) practice questions from various textbooks. Although, this lecture is based on Substitution method but there are also some questions based on previous lecture of Direct Integration.

## NCERT Exercise 7.4

This section has complete explanation of concepts based on NCERT Exericse 7.4 with each and every NCERT solutions.